Question

Consider the line - 7x-6y = 4.

Answer 1

Answer:

A parallel line would have a slope of $-\frac{7}{6}$ while a perpendicular would have a slope of $\frac{6}{7}$.

Step-by-step explanation:

Convert this equation to slope-intercept format ($y=mx+b$):

$-7x-6y=4\\-7x+7x-6y=4+7x\\-6y=7x+4\\\frac{-6y}{-6} =\frac{7x}{-6}+\frac{4}{-6} \\y = -\frac{7}{6}x-\frac{2}{3}$

In this case, your slope is $-\frac{7}{6}$.

A parallel line, by definition, will have the same slope as your original line; otherwise, the lines would eventually touch, which would render them not parallel.

A perpendicular line, on the other hand, must form four 90-degree angles when it intersects the original line, that is, it must cross it at an exact slope; that slope is the opposite reciprocal of the slope for the original line. Simply put, invert the sign and flip the fraction. In this case:

$Original = -\frac{7}{6}\\Perpendicular = \frac{6}{7}$